The sudden death of Gaussian EPR steering is different from that of the
Gaussian entanglement, which is characterised by the positive partial
transposition (PPT) criterion [1]} (see Methods for details). Figure 5
shows the entanglement and steering region parameterized by transmission
efficiency and excess noise, where the purple region represents the two-way
steering region, the cyan region represents the one-way steering region of \(\mathcal {G}^{A\rightarrow B}\) , the light red region represents the one-way
steering region of \(\mathcal {G}^{B\rightarrow A}\) , and the yellow region
represents the entanglement without steering region, respectively. Firstly,
the direction of the EPR steering is changed with the increase of excess
noise which is not the case in entanglement sudden death. The sudden death
of EPR steering and entanglement happens when there is excess noise in the
quantum channel. For a pure \(-3\)  dB TMSS, the direction of EPR steering is
changed when the excess noise is 0.25 times of vacuum noise. This result
comes from the intrinsic asymmetric character of EPR steering. Secondly, it
is obvious that the sudden death of Gaussian EPR steering happens earlier
than that of the entanglement with same excess noise level. Thirdly,
different from entanglement, the sudden death of Gaussian EPR steering in a
noisy channel is directional.
